Solve for $x$ and $y$ using substitution. ${4x+6y = 10}$ ${x = -2y+2}$
Solution: Since $x$ has already been solved for, substitute $-2y+2$ for $x$ in the first equation. ${4}{(-2y+2)}{+ 6y = 10}$ Simplify and solve for $y$ $-8y+8 + 6y = 10$ $-2y+8 = 10$ $-2y+8{-8} = 10{-8}$ $-2y = 2$ $\dfrac{-2y}{{-2}} = \dfrac{2}{{-2}}$ ${y = -1}$ Now that you know ${y = -1}$ , plug it back into $\thinspace {x = -2y+2}\thinspace$ to find $x$ ${x = -2}{(-1)}{ + 2}$ $x = 2 + 2$ ${x = 4}$ You can also plug ${y = -1}$ into $\thinspace {4x+6y = 10}\thinspace$ and get the same answer for $x$ : ${4x + 6}{(-1)}{= 10}$ ${x = 4}$